A model for rank one measure preserving transformations

2013/08/10 by Aaron Hill, Gao, Su, Hill, Aaron
Computer Science · Mathematics · #37 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1308.2340

openalex publication_date 2013/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a model for rank one measure preserving transformations in the sense of [2]. This is done by defining a new Polish topology on the space of codes, which are infinite rank one words, for symbolic rank one systems. We establish that this space of codes has the same generic dynamical properties as the space of (rank one) measure preserving transformations on the unit interval.

Related

• On measure-preserving rank one transformations
• Constructive symbolic presentations of rank one measure-preserving systems
• Topological isomorphism for rank-1 systems
• Bounded rank-one transformations
• On Mixing Rank One Infinite Transformations